SOLUTION: A school district is combining 2 schools that will have a total of 1000 students, 42% of whom are african american. 90% of one school is african american and 10% of the other is af

Question 184467: A school district is combining 2 schools that will have a total of 1000 students, 42% of whom are african american. 90% of one school is african american and 10% of the other is african american. How may students are in each school.
I've tried solving it several different ways x/2 + 420 = 1000 and x + y - 420 = 1000 for example and just can't figure this out! Please help - thank you very much!
Answer by solver91311(12126) (Show Source):
You can put this solution on YOUR website!

If 42% of the new school is african-american, then out of the 1000 students at the new school, 420 are african-american.

If x represents the number of students at one school and y represents the number of students at the second school. We can establish three things:

1. The sum of the students from the 2 schools must equal 1000:

(1)

2. 90% of the first school is african-american, so you can say the number of african american students at school 1 is:

3. Likewise, the number of african american students at the second school is:

And we know that 420 is the sum of the african-americans at both schools, so:

(2)

Now (1) and (2) form a system of linear equations that can be solved by either substitution or elimination.

John